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Beliebt Rechnen >

derivative 2tsin(t)

Lösung

ableitung von

2 t sin (t)

Lösung

2 (sin (t) + t cos (t))

Schritte zur Lösung

\frac{d}{d t} (2 t sin (t))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d t} (t sin (t))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = t, g = sin (t)

= 2 (\frac{d t}{d t} sin (t) + \frac{d}{d t} (sin (t)) t)

\frac{d t}{d t} = 1

\frac{d}{d t} (sin (t)) = cos (t)

= 2 (1 \cdot sin (t) + cos (t) t)

Vereinfache

= 2 (sin (t) + t cos (t))

Graph

Beliebte Beispiele

derivative of (3x^2+2y^2/((x-2y)^2))

\frac{d}{d x} (\frac{3 x ^{2} + 2 y ^{2}}{( x - 2 y ) ^{2}})

tangent f(x)=sqrt(x),\at x= 1/9

t an g e n t f (x) = x, at x = \frac{1}{9}

derivative of sin(sqrt(2x))

\frac{d}{d x} (sin (2 x))

derivative of cos((pix^7))

\frac{d}{d x} (cos ((π x)^{7}))

derivative of (x^3-3x^4)

\frac{d}{d x} ((x^{3} - 3 x)^{4})